The acceleration due to gravity at a height of 7 ~km above the earth is the same as at a depth d below the surface of the earth. Then d is

Step-by-step solution

The acceleration due to gravity at a height h above the surface of the earth is given by g_h = g (1 - 2h R ) , where g is the acceleration due to gravity at the surface and R is the radius of the earth. The acceleration due to gravity at a depth d below the surface of the earth is given by g_d = g (1 - d R ) . Given that g_h = g_d , we equate the two expressions: g (1 - 2h R ) = g (1 - d R ) 1 - 2h R = 1 - d R 2h R = d R d = 2h Given h = 7 km , we have d = 2 7 km = 14 km . Answer: 14 km